We now show the explicit transformation to polar coordinates, and then to HEFT, of the
SMEFT electroweak Lagrangian of Eq. (REF ) in terms of the \(SU(2)\)  doublet \(H\) , neglecting the gauge couplings and \(V(H)\)  as is appropriate for TeV-scale physics \(E\gg m_{h,W,Z}\)  , following the discussion in [1]}, with
\( \mathcal {L}_{\rm SMEFT}= A(|H|^2)| \partial H|^2+\frac{1}{2}B(|H|^2)(\partial (|H|^2))^2\) .
This is achieved by decomposing the doublet \(H\)  of the SMEFT framework in the spherical polar coordinates of Eq. (REF ),
\(H &=& \left(1+\frac{h}{v}\right)\, U(\omega ) \, \langle H\rangle \, ,\) 
